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I have collected data on how many events occur (as counts) across three groups: control, sham, experimental. I have also collected continuous data such as body mass, wing length, along with age. My main aim is to determine if the treatments have affected the counts received by each group. Would a Kruskal-Wallis be sufficient to analyse this? I know Poisson regression is also used with count data but interpretation gets difficult with the different kinds of variables used as predictors (meaning : No of events ~ groups + age + body mass+ wing length as the formula) . Or would a chi-square test be most appropriate?

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  • $\begingroup$ If you want to have a relatively complex model, as you write, like noOfEvents ~ groups + age + bodyMass+ wingLength, then Kruskal-Wallis won't cut it. There's nothing particularly difficult about formulating such a model using maybe Poisson regression or negative binomial regression. $\endgroup$ Oct 16, 2021 at 15:22

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Like the Wilcoxon test and the proportional odds ordinal logistic model, the Kruskal-Wallis test does not assume a distribution of Y for any one of the groups. It just assumes, to have optimal power, how the shapes of your three distributions are connected to each other. So the K-W test has far fewer assumptions than Poisson regression and would be a good choice here. It generalizes to the proportional odds model so you can also use that, which handles ties a little better and would also allow for covariate adjustment.

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